The subgrid‐scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.

A proposed modification of the Germano subgrid‐scale closure method

The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the

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Immersed boundary methods

A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y
3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

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Subgrid-scale stress modelling based on the square of the velocity gradient tensor

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.

/pdf/a-new-version-of-detached-eddy-simulation-resistant-to-yuj0rxxfha.pdf

A new version of detached-eddy simulation, resistant to ambiguous grid densities

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations

Direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles. The hydrodynamic field was computed using 643 points and a statistically stationary flow was obtained by forcing the low‐wave‐number components of the velocity field. The particles used in the simulations were time advanced according to Stokes drag law and were also assumed to be much more dense than the fluid. Properties of the particle cloud were obtained by following the trajectories of 1 000 000 particles through the simulated flow fields. Three values of the ratio of the particle time constant to large‐scale turbulence time scale were used in the simulations: 0.075, 0.15, and 0.52. The simulations show that the particles collect preferentially in regions of low vorticity and high strain rate. This preferential collection was most pronounced for the intermediate particle time constant (0.15) and it was also found that the instantaneous number density was as much as 25 times the mean value for these simulations. The fact that dense particles collect in regions of low vorticity and high strain in turn implies that turbulence may actually inhibit rather than enhance mixing of particles.

Preferential concentration of particles by turbulence

The effect of turbulence on particle concentration fields and the modification of turbulence by particles has been investigated using direct numerical simulations of isotropic turbulence. The particle motion was computed using Stokes’ law of resistance and it was also assumed the particle volume fraction was negligible. For simulations in which the particles do not modify the turbulence field it was found that light particles collect preferentially in regions of low vorticity and high strain rate. For increased mass loading the particle field attenuated an increasing fraction of the turbulence energy. Examination of the spatial energy spectra showed that the fraction of turbulence kinetic energy in the high wave numbers was increased relative to the energy in the low wave numbers for increasing values of the mass loading. It was also found that the turbulence field was modified differently by light particles than by heavy particles because of the preferential collection of the light particles in low‐vorticity, high‐strain‐rate regions. Correlation coefficients between the second invariant of the deformation tensor and pressure showed little sensitivity to increased loading while correlations between enstrophy and pressure were decreased more by the light particles than by the heavy particles for increased mass loading.

Kyle D. Squires

Papers

A new version of detached-eddy simulation, resistant to ambiguous grid densities

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations

Preferential concentration of particles by turbulence

Particle response and turbulence modification in isotropic turbulence